I come, originally, from that part of the world and never heard any folk songs sung there - apart from those sung in local Folk Clubs. A couple of friends, who were serious folk song scholars, collected a handful of songs in the late 1960s - but those all belonged to the 'standard' English folk song repertoire. I very much doubt that any songs about 'Black Shuck' or Fenland before drainage or duck hunting or Vermuyden or Oliver Cromwell or Whittlesey, Ramsey or Wisbech ever existed (or if they did they have been completely lost).

What usually happens, when people are searching for regional songs, is that they encounter a lot of poems set to music or recent songs written by local folk song enthusiasts and fondly imagine that those are the songs that they are looking for.